Problem: What number can be added to both the numerator and denominator of $\frac{3}{5}$ so that the resulting fraction will be equivalent to $\frac{5}{6}$?
Explanation: We seek the number $n$ such that $\frac{3+n}{5+n} = \frac{5}{6}$.  Multiplying both sides by $5+n$ and by 6 gives $(3+n)(6) = 5(5+n)$.  Expanding both sides gives $18 + 6n = 25 + 5n$.  Simplifying this equation gives $n = \boxed{7}$.